LMFDB - Embedded newform 256.2.i.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	256.17
Dual form			256.2.i.a.241.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.894167 + 1.33822i) q^{3} +(0.631428 + 3.17440i) q^{5} +(0.127129 + 0.306917i) q^{7} +(0.156763 - 0.378460i) q^{9} +O(q^{10})$	\(q+(0.894167 + 1.33822i) q^{3} +(0.631428 + 3.17440i) q^{5} +(0.127129 + 0.306917i) q^{7} +(0.156763 - 0.378460i) q^{9} +(-3.52624 - 2.35616i) q^{11} +(-0.690738 + 3.47257i) q^{13} +(-3.68343 + 3.68343i) q^{15} +(-2.19074 - 2.19074i) q^{17} +(6.74130 + 1.34093i) q^{19} +(-0.297047 + 0.444562i) q^{21} +(0.672631 + 0.278613i) q^{23} +(-5.05873 + 2.09540i) q^{25} +(5.38223 - 1.07059i) q^{27} +(7.95458 - 5.31508i) q^{29} +0.880409i q^{31} -6.82567i q^{33} +(-0.894006 + 0.597355i) q^{35} +(-5.44280 + 1.08264i) q^{37} +(-5.26469 + 2.18070i) q^{39} +(3.05507 + 1.26545i) q^{41} +(-1.59134 + 2.38161i) q^{43} +(1.30037 + 0.258659i) q^{45} +(-3.23201 - 3.23201i) q^{47} +(4.87171 - 4.87171i) q^{49} +(0.972796 - 4.89058i) q^{51} +(-7.45949 - 4.98427i) q^{53} +(5.25283 - 12.6815i) q^{55} +(4.23340 + 10.2203i) q^{57} +(-0.795535 - 3.99942i) q^{59} +(2.62163 + 3.92355i) q^{61} +0.136085 q^{63} -11.4595 q^{65} +(3.03636 + 4.54423i) q^{67} +(0.228601 + 1.14925i) q^{69} +(-2.69641 - 6.50971i) q^{71} +(4.10841 - 9.91857i) q^{73} +(-7.32745 - 4.89605i) q^{75} +(0.274857 - 1.38180i) q^{77} +(1.54370 - 1.54370i) q^{79} +(5.37632 + 5.37632i) q^{81} +(-14.5352 - 2.89122i) q^{83} +(5.57100 - 8.33759i) q^{85} +(14.2254 + 5.89237i) q^{87} +(-1.64085 + 0.679662i) q^{89} +(-1.15360 + 0.229466i) q^{91} +(-1.17818 + 0.787233i) q^{93} +22.2463i q^{95} +2.43552i q^{97} +(-1.44450 + 0.965182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.894167	+	1.33822i	0.516248	+	0.772619i	0.994403	−	0.105656i	$-0.0336943\pi$
$3$	0.894167	+	1.33822i	0.516248	+	0.772619i	−0.478155	+	0.878276i	$0.658694\pi$
$4$		0			0
$5$	0.631428	+	3.17440i	0.282383	+	1.41964i	0.818021	+	0.575188i	$0.195071\pi$
$5$	0.631428	+	3.17440i	0.282383	+	1.41964i	−0.535638	+	0.844448i	$0.679929\pi$
$6$		0			0
$7$	0.127129	+	0.306917i	0.0480503	+	0.116004i	0.946082	−	0.323927i	$-0.105003\pi$
$7$	0.127129	+	0.306917i	0.0480503	+	0.116004i	−0.898032	+	0.439930i	$0.855003\pi$
$8$		0			0
$9$	0.156763	−	0.378460i	0.0522544	−	0.126153i
$10$		0			0
$11$	−3.52624	−	2.35616i	−1.06320	−	0.710409i	−0.104414	−	0.994534i	$-0.533297\pi$
$11$	−3.52624	−	2.35616i	−1.06320	−	0.710409i	−0.958787	+	0.284125i	$0.908297\pi$
$12$		0			0
$13$	−0.690738	+	3.47257i	−0.191576	+	0.963118i	0.758636	+	0.651515i	$0.225866\pi$
$13$	−0.690738	+	3.47257i	−0.191576	+	0.963118i	−0.950212	+	0.311604i	$0.899134\pi$
$14$		0			0
$15$	−3.68343	+	3.68343i	−0.951059	+	0.951059i
$16$		0			0
$17$	−2.19074	−	2.19074i	−0.531333	−	0.531333i	0.389636	−	0.920969i	$-0.372601\pi$
$17$	−2.19074	−	2.19074i	−0.531333	−	0.531333i	−0.920969	+	0.389636i	$0.872601\pi$
$18$		0			0
$19$	6.74130	+	1.34093i	1.54656	+	0.307630i	0.893285	−	0.449491i	$-0.148395\pi$
$19$	6.74130	+	1.34093i	1.54656	+	0.307630i	0.653275	+	0.757121i	$0.273395\pi$
$20$		0			0
$21$	−0.297047	+	0.444562i	−0.0648209	+	0.0970113i
$22$		0			0
$23$	0.672631	+	0.278613i	0.140253	+	0.0580948i	0.451706	−	0.892167i	$-0.350816\pi$
$23$	0.672631	+	0.278613i	0.140253	+	0.0580948i	−0.311453	+	0.950262i	$0.600816\pi$
$24$		0			0
$25$	−5.05873	+	2.09540i	−1.01175	+	0.419079i
$26$		0			0
$27$	5.38223	−	1.07059i	1.03581	−	0.206036i
$28$		0			0
$29$	7.95458	−	5.31508i	1.47713	−	0.986985i	0.483371	−	0.875415i	$-0.339412\pi$
$29$	7.95458	−	5.31508i	1.47713	−	0.986985i	0.993757	−	0.111570i	$-0.0355879\pi$
$30$		0			0
$31$			0.880409i			0.158126i	0.996870	+	0.0790630i	$0.0251928\pi$
$31$			0.880409i			0.158126i	−0.996870	+	0.0790630i	$0.974807\pi$
$32$		0			0
$33$		−	6.82567i		−	1.18820i
$34$		0			0
$35$	−0.894006	+	0.597355i	−0.151115	+	0.100972i
$36$		0			0
$37$	−5.44280	+	1.08264i	−0.894791	+	0.177985i	−0.621006	−	0.783806i	$-0.713276\pi$
$37$	−5.44280	+	1.08264i	−0.894791	+	0.177985i	−0.273785	+	0.961791i	$0.588276\pi$
$38$		0			0
$39$	−5.26469	+	2.18070i	−0.843025	+	0.349192i
$40$		0			0
$41$	3.05507	+	1.26545i	0.477122	+	0.197631i	0.608267	−	0.793733i	$-0.291865\pi$
$41$	3.05507	+	1.26545i	0.477122	+	0.197631i	−0.131144	+	0.991363i	$0.541865\pi$
$42$		0			0
$43$	−1.59134	+	2.38161i	−0.242677	+	0.363192i	−0.932735	−	0.360562i	$-0.882585\pi$
$43$	−1.59134	+	2.38161i	−0.242677	+	0.363192i	0.690058	+	0.723754i	$0.257585\pi$
$44$		0			0
$45$	1.30037	+	0.258659i	0.193848	+	0.0385587i
$46$		0			0
$47$	−3.23201	−	3.23201i	−0.471438	−	0.471438i	0.430942	−	0.902380i	$-0.358181\pi$
$47$	−3.23201	−	3.23201i	−0.471438	−	0.471438i	−0.902380	+	0.430942i	$0.858181\pi$
$48$		0			0
$49$	4.87171	−	4.87171i	0.695959	−	0.695959i
$50$		0			0
$51$	0.972796	−	4.89058i	0.136219	−	0.684818i
$52$		0			0
$53$	−7.45949	−	4.98427i	−1.02464	−	0.684643i	−0.0747420	−	0.997203i	$-0.523813\pi$
$53$	−7.45949	−	4.98427i	−1.02464	−	0.684643i	−0.949898	+	0.312560i	$0.898813\pi$
$54$		0			0
$55$	5.25283	−	12.6815i	0.708291	−	1.70997i
$56$		0			0
$57$	4.23340	+	10.2203i	0.560727	+	1.35372i
$58$		0			0
$59$	−0.795535	−	3.99942i	−0.103570	−	0.520681i	−0.997387	−	0.0722484i	$-0.976983\pi$
$59$	−0.795535	−	3.99942i	−0.103570	−	0.520681i	0.893817	−	0.448432i	$-0.148017\pi$
$60$		0			0
$61$	2.62163	+	3.92355i	0.335666	+	0.502359i	0.960455	−	0.278434i	$-0.0898153\pi$
$61$	2.62163	+	3.92355i	0.335666	+	0.502359i	−0.624790	+	0.780793i	$0.714815\pi$
$62$		0			0
$63$	0.136085			0.0171451
$64$		0			0
$65$	−11.4595			−1.42138
$66$		0			0
$67$	3.03636	+	4.54423i	0.370950	+	0.555166i	0.969241	−	0.246113i	$-0.0791533\pi$
$67$	3.03636	+	4.54423i	0.370950	+	0.555166i	−0.598291	+	0.801279i	$0.704153\pi$
$68$		0			0
$69$	0.228601	+	1.14925i	0.0275203	+	0.138354i
$70$		0			0
$71$	−2.69641	−	6.50971i	−0.320005	−	0.772561i	−0.999253	−	0.0386517i	$-0.987694\pi$
$71$	−2.69641	−	6.50971i	−0.320005	−	0.772561i	0.679248	−	0.733909i	$-0.262306\pi$
$72$		0			0
$73$	4.10841	−	9.91857i	0.480853	−	1.16088i	−0.478352	−	0.878168i	$-0.658766\pi$
$73$	4.10841	−	9.91857i	0.480853	−	1.16088i	0.959205	−	0.282713i	$-0.0912344\pi$
$74$		0			0
$75$	−7.32745	−	4.89605i	−0.846101	−	0.565347i
$76$		0			0
$77$	0.274857	−	1.38180i	0.0313229	−	0.157471i
$78$		0			0
$79$	1.54370	−	1.54370i	0.173680	−	0.173680i	−0.614914	−	0.788594i	$-0.710809\pi$
$79$	1.54370	−	1.54370i	0.173680	−	0.173680i	0.788594	+	0.614914i	$0.210809\pi$
$80$		0			0
$81$	5.37632	+	5.37632i	0.597369	+	0.597369i
$82$		0			0
$83$	−14.5352	−	2.89122i	−1.59544	−	0.317353i	−0.684221	−	0.729275i	$-0.739858\pi$
$83$	−14.5352	−	2.89122i	−1.59544	−	0.317353i	−0.911219	+	0.411922i	$0.864858\pi$
$84$		0			0
$85$	5.57100	−	8.33759i	0.604260	−	0.904339i
$86$		0			0
$87$	14.2254	+	5.89237i	1.52513	+	0.631729i
$88$		0			0
$89$	−1.64085	+	0.679662i	−0.173930	+	0.0720441i	−0.467949	−	0.883755i	$-0.655007\pi$
$89$	−1.64085	+	0.679662i	−0.173930	+	0.0720441i	0.294019	+	0.955799i	$0.405007\pi$
$90$		0			0
$91$	−1.15360	+	0.229466i	−0.120931	+	0.0240546i
$92$		0			0
$93$	−1.17818	+	0.787233i	−0.122171	+	0.0816322i
$94$		0			0
$95$			22.2463i			2.28242i
$96$		0			0
$97$			2.43552i			0.247289i	0.992327	+	0.123645i	$0.0394583\pi$
$97$			2.43552i			0.247289i	−0.992327	+	0.123645i	$0.960542\pi$
$98$		0			0
$99$	−1.44450	+	0.965182i	−0.145177	+	0.0970044i
$100$		0			0
$101$	−0.776702	+	0.154496i	−0.0772847	+	0.0153729i	−0.233581	−	0.972337i	$-0.575044\pi$
$101$	−0.776702	+	0.154496i	−0.0772847	+	0.0153729i	0.156296	+	0.987710i	$0.450044\pi$
$102$		0			0
$103$	5.94004	−	2.46045i	0.585290	−	0.242435i	−0.0703329	−	0.997524i	$-0.522406\pi$
$103$	5.94004	−	2.46045i	0.585290	−	0.242435i	0.655623	+	0.755089i	$0.272406\pi$
$104$		0			0
$105$	−1.59878	−	0.662237i	−0.156025	−	0.0646277i
$106$		0			0
$107$	−3.42296	+	5.12283i	−0.330910	+	0.495242i	−0.959197	−	0.282740i	$-0.908757\pi$
$107$	−3.42296	+	5.12283i	−0.330910	+	0.495242i	0.628286	+	0.777982i	$0.283757\pi$
$108$		0			0
$109$	−9.42451	−	1.87465i	−0.902704	−	0.179559i	−0.278148	−	0.960538i	$-0.589720\pi$
$109$	−9.42451	−	1.87465i	−0.902704	−	0.179559i	−0.624557	+	0.780979i	$0.714720\pi$
$110$		0			0
$111$	−6.31558	−	6.31558i	−0.599448	−	0.599448i
$112$		0			0
$113$	−4.53709	+	4.53709i	−0.426814	+	0.426814i	−0.887541	−	0.460728i	$-0.847588\pi$
$113$	−4.53709	+	4.53709i	−0.426814	+	0.426814i	0.460728	+	0.887541i	$0.347588\pi$
$114$		0			0
$115$	−0.459712	+	2.31113i	−0.0428683	+	0.215514i
$116$		0			0
$117$	1.20595	+	0.805788i	0.111490	+	0.0744951i
$118$		0			0
$119$	0.393869	−	0.950883i	0.0361059	−	0.0871673i
$120$		0			0
$121$	2.67337	+	6.45409i	0.243034	+	0.586735i
$122$		0			0
$123$	1.03830	+	5.21988i	0.0936202	+	0.470660i
$124$		0			0
$125$	−0.855086	−	1.27973i	−0.0764812	−	0.114462i
$126$		0			0
$127$	13.1460			1.16652			0.583260	−	0.812285i	$-0.301777\pi$
$127$	13.1460			1.16652			0.583260	+	0.812285i	$0.301777\pi$
$128$		0			0
$129$	−4.61004			−0.405891
$130$		0			0
$131$	8.01070	+	11.9889i	0.699898	+	1.04747i	0.995737	+	0.0922342i	$0.0294008\pi$
$131$	8.01070	+	11.9889i	0.699898	+	1.04747i	−0.295839	+	0.955238i	$0.595599\pi$
$132$		0			0
$133$	0.445462	+	2.23949i	0.0386265	+	0.194188i
$134$		0			0
$135$	6.79699	+	16.4094i	0.584992	+	1.41229i
$136$		0			0
$137$	−2.01913	+	4.87460i	−0.172506	+	0.416465i	−0.986360	−	0.164604i	$-0.947365\pi$
$137$	−2.01913	+	4.87460i	−0.172506	+	0.416465i	0.813854	+	0.581069i	$0.197365\pi$
$138$		0			0
$139$	4.06094	+	2.71344i	0.344445	+	0.230151i	0.715744	−	0.698363i	$-0.246088\pi$
$139$	4.06094	+	2.71344i	0.344445	+	0.230151i	−0.371299	+	0.928513i	$0.621088\pi$
$140$		0			0
$141$	1.43517	−	7.21509i	0.120863	−	0.607620i
$142$		0			0
$143$	10.6176	−	10.6176i	0.887891	−	0.887891i
$144$		0			0
$145$	21.8949	+	21.8949i	1.81828	+	1.81828i
$146$		0			0
$147$	10.8755	+	2.16328i	0.896998	+	0.178424i
$148$		0			0
$149$	−5.32373	+	7.96752i	−0.436137	+	0.652725i	−0.982810	−	0.184622i	$-0.940894\pi$
$149$	−5.32373	+	7.96752i	−0.436137	+	0.652725i	0.546673	+	0.837346i	$0.315894\pi$
$150$		0			0
$151$	−15.2438	−	6.31419i	−1.24052	−	0.513841i	−0.336645	−	0.941632i	$-0.609292\pi$
$151$	−15.2438	−	6.31419i	−1.24052	−	0.513841i	−0.903878	+	0.427791i	$0.859292\pi$
$152$		0			0
$153$	−1.17254	+	0.485680i	−0.0947939	+	0.0392649i
$154$		0			0
$155$	−2.79477	+	0.555915i	−0.224481	+	0.0446521i
$156$		0			0
$157$	0.183668	−	0.122723i	0.0146583	−	0.00979438i	−0.548219	−	0.836335i	$-0.684694\pi$
$157$	0.183668	−	0.122723i	0.0146583	−	0.00979438i	0.562878	+	0.826540i	$0.309694\pi$
$158$		0			0
$159$		−	14.4392i		−	1.14510i
$160$		0			0
$161$			0.241862i			0.0190614i
$162$		0			0
$163$	−14.8711	+	9.93653i	−1.16479	+	0.778289i	−0.978912	−	0.204283i	$-0.934514\pi$
$163$	−14.8711	+	9.93653i	−1.16479	+	0.778289i	−0.185880	+	0.982572i	$0.559514\pi$
$164$		0			0
$165$	21.6674	−	4.30992i	1.68681	−	0.335527i
$166$		0			0
$167$	−16.9720	+	7.03005i	−1.31334	+	0.544001i	−0.925856	−	0.377877i	$-0.876654\pi$
$167$	−16.9720	+	7.03005i	−1.31334	+	0.544001i	−0.387480	+	0.921878i	$0.626654\pi$
$168$		0			0
$169$	0.428795	+	0.177613i	0.0329842	+	0.0136625i
$170$		0			0
$171$	1.56427	−	2.34110i	0.119623	−	0.179029i
$172$		0			0
$173$	−12.9081	−	2.56758i	−0.981384	−	0.195210i	−0.321773	−	0.946817i	$-0.604279\pi$
$173$	−12.9081	−	2.56758i	−0.981384	−	0.195210i	−0.659611	+	0.751607i	$0.729279\pi$
$174$		0			0
$175$	−1.28623	−	1.28623i	−0.0972296	−	0.0972296i
$176$		0			0
$177$	4.64075	−	4.64075i	0.348820	−	0.348820i
$178$		0			0
$179$	4.41588	−	22.2001i	0.330058	−	1.65932i	−0.358046	−	0.933704i	$-0.616557\pi$
$179$	4.41588	−	22.2001i	0.330058	−	1.65932i	0.688105	−	0.725612i	$-0.258443\pi$
$180$		0			0
$181$	−12.2894	−	8.21153i	−0.913466	−	0.610358i	0.00751269	−	0.999972i	$-0.497609\pi$
$181$	−12.2894	−	8.21153i	−0.913466	−	0.610358i	−0.920978	+	0.389613i	$0.872609\pi$
$182$		0			0
$183$	−2.90638	+	7.01663i	−0.214846	+	0.518684i
$184$		0			0
$185$	−6.87347	−	16.5940i	−0.505348	−	1.22002i
$186$		0			0
$187$	2.56335	+	12.8868i	0.187450	+	0.942377i
$188$		0			0
$189$	1.01282	+	1.51580i	0.0736720	+	0.110258i
$190$		0			0
$191$	−6.69554			−0.484472			−0.242236	−	0.970217i	$-0.577881\pi$
$191$	−6.69554			−0.484472			−0.242236	+	0.970217i	$0.577881\pi$
$192$		0			0
$193$	3.13547			0.225696			0.112848	−	0.993612i	$-0.464003\pi$
$193$	3.13547			0.225696			0.112848	+	0.993612i	$0.464003\pi$
$194$		0			0
$195$	−10.2467	−	15.3353i	−0.733782	−	1.09818i
$196$		0			0
$197$	3.05543	+	15.3607i	0.217690	+	1.09440i	0.922793	+	0.385297i	$0.125901\pi$
$197$	3.05543	+	15.3607i	0.217690	+	1.09440i	−0.705102	+	0.709106i	$0.749099\pi$
$198$		0			0
$199$	1.63780	+	3.95399i	0.116100	+	0.280291i	0.971238	−	0.238109i	$-0.0765277\pi$
$199$	1.63780	+	3.95399i	0.116100	+	0.280291i	−0.855138	+	0.518400i	$0.826528\pi$
$200$		0			0
$201$	−3.36615	+	8.12661i	−0.237430	+	0.573207i
$202$		0			0
$203$	2.64255	+	1.76569i	0.185471	+	0.123927i
$204$		0			0
$205$	−2.08800	+	10.4971i	−0.145832	+	0.733148i
$206$		0			0
$207$	0.210888	−	0.210888i	0.0146577	−	0.0146577i
$208$		0			0
$209$	−20.6120	−	20.6120i	−1.42576	−	1.42576i
$210$		0			0
$211$	−20.2759	−	4.03313i	−1.39585	−	0.277652i	−0.560857	−	0.827912i	$-0.689528\pi$
$211$	−20.2759	−	4.03313i	−1.39585	−	0.277652i	−0.834993	+	0.550261i	$0.814528\pi$
$212$		0			0
$213$	6.30036	−	9.42916i	0.431694	−	0.646075i
$214$		0			0
$215$	−8.56501	−	3.54775i	−0.584129	−	0.241954i
$216$		0			0
$217$	−0.270212	+	0.111926i	−0.0183432	+	0.00759801i
$218$		0			0
$219$	16.9468	−	3.37093i	1.14516	−	0.227786i
$220$		0			0
$221$	9.12074	−	6.09428i	0.613527	−	0.409946i
$222$		0			0
$223$		−	18.1462i		−	1.21516i	−0.794258	−	0.607581i	$-0.792140\pi$
$223$		−	18.1462i		−	1.21516i	0.794258	−	0.607581i	$-0.207860\pi$
$224$		0			0
$225$			2.24301i			0.149534i
$226$		0			0
$227$	13.4874	−	9.01200i	0.895191	−	0.598148i	−0.0206063	−	0.999788i	$-0.506560\pi$
$227$	13.4874	−	9.01200i	0.895191	−	0.598148i	0.915798	+	0.401640i	$0.131560\pi$
$228$		0			0
$229$	1.15657	−	0.230055i	0.0764281	−	0.0152025i	−0.156728	−	0.987642i	$-0.550095\pi$
$229$	1.15657	−	0.230055i	0.0764281	−	0.0152025i	0.233156	+	0.972439i	$0.425095\pi$
$230$		0			0
$231$	2.09492	−	0.867742i	0.137835	−	0.0570933i
$232$		0			0
$233$	−3.25867	−	1.34979i	−0.213483	−	0.0884274i	0.273379	−	0.961906i	$-0.411859\pi$
$233$	−3.25867	−	1.34979i	−0.213483	−	0.0884274i	−0.486862	+	0.873479i	$0.661859\pi$
$234$		0			0
$235$	8.21893	−	12.3005i	0.536144	−	0.802396i
$236$		0			0
$237$	3.44614	+	0.685479i	0.223851	+	0.0445266i
$238$		0			0
$239$	5.54582	+	5.54582i	0.358729	+	0.358729i	0.863344	−	0.504615i	$-0.168366\pi$
$239$	5.54582	+	5.54582i	0.358729	+	0.358729i	−0.504615	+	0.863344i	$0.668366\pi$
$240$		0			0
$241$	−5.98668	+	5.98668i	−0.385636	+	0.385636i	−0.873128	−	0.487492i	$-0.837912\pi$
$241$	−5.98668	+	5.98668i	−0.385636	+	0.385636i	0.487492	+	0.873128i	$0.337912\pi$
$242$		0			0
$243$	0.824430	−	4.14469i	0.0528872	−	0.265882i
$244$		0			0
$245$	18.5409	+	12.3886i	1.18454	+	0.791481i
$246$		0			0
$247$	−9.31293	+	22.4834i	−0.592568	+	1.43058i
$248$		0			0
$249$	−9.12778	−	22.0364i	−0.578450	−	1.39650i
$250$		0			0
$251$	−0.437354	−	2.19873i	−0.0276055	−	0.138782i	0.964525	−	0.263993i	$-0.0850395\pi$
$251$	−0.437354	−	2.19873i	−0.0276055	−	0.138782i	−0.992130	+	0.125210i	$0.960039\pi$
$252$		0			0
$253$	−1.71540	−	2.56728i	−0.107846	−	0.161404i
$254$		0			0
$255$	16.1389			1.01066
$256$		0			0
$257$	19.0558			1.18867			0.594334	−	0.804218i	$-0.297416\pi$
$257$	19.0558			1.18867			0.594334	+	0.804218i	$0.297416\pi$
$258$		0			0
$259$	−1.02422	−	1.53285i	−0.0636419	−	0.0952469i
$260$		0			0
$261$	−0.764559	−	3.84370i	−0.0473250	−	0.237919i
$262$		0			0
$263$	−2.42000	−	5.84240i	−0.149224	−	0.360258i	0.831538	−	0.555468i	$-0.187461\pi$
$263$	−2.42000	−	5.84240i	−0.149224	−	0.360258i	−0.980761	+	0.195211i	$0.937461\pi$
$264$		0			0
$265$	11.1120	−	26.8266i	0.682602	−	1.64795i
$266$		0			0
$267$	−2.37673	−	1.58808i	−0.145453	−	0.0971889i
$268$		0			0
$269$	−2.01219	+	10.1159i	−0.122685	+	0.616780i	0.869697	+	0.493585i	$0.164314\pi$
$269$	−2.01219	+	10.1159i	−0.122685	+	0.616780i	−0.992383	+	0.123195i	$0.960686\pi$
$270$		0			0
$271$	−4.18042	+	4.18042i	−0.253942	+	0.253942i	−0.822585	−	0.568642i	$-0.807469\pi$
$271$	−4.18042	+	4.18042i	−0.253942	+	0.253942i	0.568642	+	0.822585i	$0.307469\pi$
$272$		0			0
$273$	−1.33859	−	1.33859i	−0.0810152	−	0.0810152i
$274$		0			0
$275$	22.7754	+	4.53031i	1.37341	+	0.273188i
$276$		0			0
$277$	−1.05525	+	1.57930i	−0.0634040	+	0.0948909i	−0.861817	−	0.507220i	$-0.830673\pi$
$277$	−1.05525	+	1.57930i	−0.0634040	+	0.0948909i	0.798413	+	0.602110i	$0.205673\pi$
$278$		0			0
$279$	0.333199	+	0.138016i	0.0199481	+	0.00826278i
$280$		0			0
$281$	20.6297	−	8.54511i	1.23067	−	0.509759i	0.329881	−	0.944023i	$-0.392991\pi$
$281$	20.6297	−	8.54511i	1.23067	−	0.509759i	0.900786	+	0.434264i	$0.142991\pi$
$282$		0			0
$283$	−0.153600	+	0.0305529i	−0.00913055	+	0.00181618i	−0.199653	−	0.979867i	$-0.563982\pi$
$283$	−0.153600	+	0.0305529i	−0.00913055	+	0.00181618i	0.190523	+	0.981683i	$0.438982\pi$
$284$		0			0
$285$	−29.7703	+	19.8919i	−1.76344	+	1.17829i
$286$		0			0
$287$			1.09853i			0.0648442i
$288$		0			0
$289$		−	7.40130i		−	0.435371i
$290$		0			0
$291$	−3.25925	+	2.17776i	−0.191060	+	0.127662i
$292$		0			0
$293$	−8.18241	+	1.62758i	−0.478022	+	0.0950844i	−0.428220	−	0.903675i	$-0.640859\pi$
$293$	−8.18241	+	1.62758i	−0.478022	+	0.0950844i	−0.0498021	+	0.998759i	$0.515859\pi$
$294$		0			0
$295$	12.1935	−	5.05070i	0.709931	−	0.294063i
$296$		0			0
$297$	−21.5015	−	8.90623i	−1.24765	−	0.516792i
$298$		0			0
$299$	−1.43212	+	2.14331i	−0.0828214	+	0.123951i
$300$		0			0
$301$	−0.933264	−	0.185638i	−0.0537924	−	0.0107000i
$302$		0			0
$303$	−0.901250	−	0.901250i	−0.0517755	−	0.0517755i
$304$		0			0
$305$	−10.7996	+	10.7996i	−0.618381	+	0.618381i
$306$		0			0
$307$	−6.67898	+	33.5775i	−0.381190	+	1.91637i	0.0187412	+	0.999824i	$0.494034\pi$
$307$	−6.67898	+	33.5775i	−0.381190	+	1.91637i	−0.399931	+	0.916545i	$0.630966\pi$
$308$		0			0
$309$	8.60400	+	5.74901i	0.489465	+	0.327050i
$310$		0			0
$311$	5.03970	−	12.1669i	0.285775	−	0.689923i	−0.714174	−	0.699968i	$-0.753198\pi$
$311$	5.03970	−	12.1669i	0.285775	−	0.689923i	0.999950	+	0.0100453i	$0.00319757\pi$
$312$		0			0
$313$	−0.161015	−	0.388724i	−0.00910110	−	0.0219720i	0.919264	−	0.393642i	$-0.128785\pi$
$313$	−0.161015	−	0.388724i	−0.00910110	−	0.0219720i	−0.928365	+	0.371670i	$0.878785\pi$
$314$		0			0
$315$	0.0859279	+	0.431989i	0.00484149	+	0.0243398i
$316$		0			0
$317$	−9.33099	−	13.9648i	−0.524081	−	0.784342i	0.471133	−	0.882062i	$-0.343845\pi$
$317$	−9.33099	−	13.9648i	−0.524081	−	0.784342i	−0.995214	+	0.0977198i	$0.968845\pi$
$318$		0			0
$319$	−40.5729			−2.27165
$320$		0			0
$321$	−9.91615			−0.553466
$322$		0			0
$323$	−11.8308	−	17.7061i	−0.658284	−	0.985192i
$324$		0			0
$325$	−3.78216	−	19.0142i	−0.209796	−	1.05472i
$326$		0			0
$327$	−5.91840	−	14.2883i	−0.327288	−	0.790144i
$328$		0			0
$329$	0.581077	−	1.40284i	0.0320358	−	0.0773413i
$330$		0			0
$331$	27.3548	+	18.2779i	1.50355	+	1.00464i	0.989120	+	0.147112i	$0.0469977\pi$
$331$	27.3548	+	18.2779i	1.50355	+	1.00464i	0.514433	+	0.857530i	$0.328002\pi$
$332$		0			0
$333$	−0.443495	+	2.22960i	−0.0243034	+	0.122181i
$334$		0			0
$335$	−12.5080	+	12.5080i	−0.683384	+	0.683384i
$336$		0			0
$337$	−1.93221	−	1.93221i	−0.105254	−	0.105254i	0.652519	−	0.757773i	$-0.273712\pi$
$337$	−1.93221	−	1.93221i	−0.105254	−	0.105254i	−0.757773	+	0.652519i	$0.773712\pi$
$338$		0			0
$339$	−10.1285	−	2.01469i	−0.550106	−	0.109423i
$340$		0			0
$341$	2.07438	−	3.10453i	0.112334	−	0.168120i
$342$		0			0
$343$	4.26297	+	1.76578i	0.230179	+	0.0953431i
$344$		0			0
$345$	−3.50385	+	1.45134i	−0.188641	+	0.0781375i
$346$		0			0
$347$	−5.95710	+	1.18494i	−0.319794	+	0.0636110i	−0.352377	−	0.935858i	$-0.614627\pi$
$347$	−5.95710	+	1.18494i	−0.319794	+	0.0636110i	0.0325833	+	0.999469i	$0.489627\pi$
$348$		0			0
$349$	−2.40994	+	1.61027i	−0.129001	+	0.0861956i	−0.618397	−	0.785866i	$-0.712217\pi$
$349$	−2.40994	+	1.61027i	−0.129001	+	0.0861956i	0.489396	+	0.872062i	$0.337217\pi$
$350$		0			0
$351$			19.4297i			1.03708i
$352$		0			0
$353$			34.9802i			1.86181i	0.365261	+	0.930905i	$0.380980\pi$
$353$			34.9802i			1.86181i	−0.365261	+	0.930905i	$0.619020\pi$
$354$		0			0
$355$	18.9619	−	12.6699i	1.00639	−	0.672449i
$356$		0			0
$357$	1.62467	−	0.323167i	0.0859868	−	0.0171038i
$358$		0			0
$359$	−11.4132	+	4.72748i	−0.602363	+	0.249507i	−0.662959	−	0.748655i	$-0.730700\pi$
$359$	−11.4132	+	4.72748i	−0.602363	+	0.249507i	0.0605961	+	0.998162i	$0.480700\pi$
$360$		0			0
$361$	26.0933	+	10.8082i	1.37333	+	0.568852i
$362$		0			0
$363$	−6.24652	+	9.34858i	−0.327857	+	0.490673i
$364$		0			0
$365$	34.0797	+	6.77888i	1.78381	+	0.354823i
$366$		0			0
$367$	7.30233	+	7.30233i	0.381178	+	0.381178i	0.871527	−	0.490348i	$-0.163130\pi$
$367$	7.30233	+	7.30233i	0.381178	+	0.381178i	−0.490348	+	0.871527i	$0.663130\pi$
$368$		0			0
$369$	0.957847	−	0.957847i	0.0498635	−	0.0498635i
$370$		0			0
$371$	0.581439	−	2.92309i	0.0301868	−	0.151759i
$372$		0			0
$373$	18.9156	+	12.6390i	0.979413	+	0.654423i	0.938695	−	0.344748i	$-0.112036\pi$
$373$	18.9156	+	12.6390i	0.979413	+	0.654423i	0.0407173	+	0.999171i	$0.487036\pi$
$374$		0			0
$375$	0.947960	−	2.28858i	0.0489525	−	0.118182i
$376$		0			0
$377$	12.9625	+	31.2942i	0.667601	+	1.61173i
$378$		0			0
$379$	−4.20965	−	21.1633i	−0.216235	−	1.08709i	−0.924512	−	0.381152i	$-0.875527\pi$
$379$	−4.20965	−	21.1633i	−0.216235	−	1.08709i	0.708277	−	0.705934i	$-0.249473\pi$
$380$		0			0
$381$	11.7547	+	17.5922i	0.602213	+	0.901276i
$382$		0			0
$383$	18.3977			0.940079			0.470039	−	0.882646i	$-0.344240\pi$
$383$	18.3977			0.940079			0.470039	+	0.882646i	$0.344240\pi$
$384$		0			0
$385$	4.55994			0.232396
$386$		0			0
$387$	0.651881	+	0.975609i	0.0331370	+	0.0495930i
$388$		0			0
$389$	−3.48084	−	17.4994i	−0.176486	−	0.887253i	−0.962963	−	0.269634i	$-0.913097\pi$
$389$	−3.48084	−	17.4994i	−0.176486	−	0.887253i	0.786477	−	0.617619i	$-0.211903\pi$
$390$		0			0
$391$	−0.863192	−	2.08393i	−0.0436535	−	0.105389i
$392$		0			0
$393$	−8.88078	+	21.4401i	−0.447976	+	1.08151i
$394$		0			0
$395$	5.87507	+	3.92560i	0.295607	+	0.197518i
$396$		0			0
$397$	2.30374	−	11.5817i	0.115621	−	0.581268i	−0.878924	−	0.476962i	$-0.841738\pi$
$397$	2.30374	−	11.5817i	0.115621	−	0.581268i	0.994545	−	0.104306i	$-0.0332621\pi$
$398$		0			0
$399$	−2.59860	+	2.59860i	−0.130093	+	0.130093i
$400$		0			0
$401$	−14.2513	−	14.2513i	−0.711677	−	0.711677i	0.255209	−	0.966886i	$-0.417856\pi$
$401$	−14.2513	−	14.2513i	−0.711677	−	0.711677i	−0.966886	+	0.255209i	$0.917856\pi$
$402$		0			0
$403$	−3.05728	−	0.608131i	−0.152294	−	0.0302932i
$404$		0			0
$405$	−13.6719	+	20.4614i	−0.679360	+	1.01673i
$406$		0			0
$407$	21.7435	+	9.00645i	1.07778	+	0.446433i
$408$		0			0
$409$	−21.7113	+	8.99313i	−1.07356	+	0.444682i	−0.848244	−	0.529605i	$-0.822340\pi$
$409$	−21.7113	+	8.99313i	−1.07356	+	0.444682i	−0.225312	+	0.974287i	$0.572340\pi$
$410$		0			0
$411$	−8.32871	+	1.65668i	−0.410825	+	0.0817182i
$412$		0			0
$413$	1.12636	−	0.752607i	0.0554243	−	0.0370334i
$414$		0			0
$415$		−	47.9660i		−	2.35456i
$416$		0			0
$417$			7.86069i			0.384940i
$418$		0			0
$419$	2.46480	−	1.64693i	0.120413	−	0.0804577i	−0.493905	−	0.869516i	$-0.664431\pi$
$419$	2.46480	−	1.64693i	0.120413	−	0.0804577i	0.614319	+	0.789058i	$0.289431\pi$
$420$		0			0
$421$	−33.4984	+	6.66325i	−1.63261	+	0.324747i	−0.924450	−	0.381303i	$-0.875475\pi$
$421$	−33.4984	+	6.66325i	−1.63261	+	0.324747i	−0.708162	+	0.706050i	$0.750475\pi$
$422$		0			0
$423$	−1.72985	+	0.716527i	−0.0841081	+	0.0348387i
$424$		0			0
$425$	15.6729	+	6.49191i	0.760245	+	0.314904i
$426$		0			0
$427$	−0.870919	+	1.30342i	−0.0421467	+	0.0630770i
$428$		0			0
$429$	23.7026	+	4.71475i	1.14437	+	0.227630i
$430$		0			0
$431$	27.7891	+	27.7891i	1.33855	+	1.33855i	0.897461	+	0.441094i	$0.145409\pi$
$431$	27.7891	+	27.7891i	1.33855	+	1.33855i	0.441094	+	0.897461i	$0.354591\pi$
$432$		0			0
$433$	19.5120	−	19.5120i	0.937689	−	0.937689i	−0.0604807	−	0.998169i	$-0.519263\pi$
$433$	19.5120	−	19.5120i	0.937689	−	0.937689i	0.998169	+	0.0604807i	$0.0192634\pi$
$434$		0			0
$435$	−9.72242	+	48.8779i	−0.466154	+	2.34352i
$436$		0			0
$437$	4.16081	+	2.78016i	0.199038	+	0.132993i
$438$		0			0
$439$	−10.7454	+	25.9416i	−0.512849	+	1.23813i	0.429370	+	0.903129i	$0.358736\pi$
$439$	−10.7454	+	25.9416i	−0.512849	+	1.23813i	−0.942219	+	0.334998i	$0.891264\pi$
$440$		0			0
$441$	−1.08004	−	2.60745i	−0.0514306	−	0.124164i
$442$		0			0
$443$	−1.40022	−	7.03938i	−0.0665264	−	0.334451i	0.933161	−	0.359459i	$-0.117039\pi$
$443$	−1.40022	−	7.03938i	−0.0665264	−	0.334451i	−0.999687	+	0.0250082i	$0.992039\pi$
$444$		0			0
$445$	−3.19360	−	4.77956i	−0.151391	−	0.226573i
$446$		0			0
$447$	−15.4226			−0.729462
$448$		0			0
$449$	9.76361			0.460773			0.230387	−	0.973099i	$-0.426001\pi$
$449$	9.76361			0.460773			0.230387	+	0.973099i	$0.426001\pi$
$450$		0			0
$451$	−7.79132	−	11.6605i	−0.366879	−	0.549073i
$452$		0			0
$453$	−5.18076	−	26.0454i	−0.243413	−	1.22372i
$454$		0			0
$455$	−1.45684	−	3.51712i	−0.0682976	−	0.164885i
$456$		0			0
$457$	−12.2635	+	29.6067i	−0.573662	+	1.38494i	0.324755	+	0.945798i	$0.394718\pi$
$457$	−12.2635	+	29.6067i	−0.573662	+	1.38494i	−0.898417	+	0.439144i	$0.855282\pi$
$458$		0			0
$459$	−14.1365	−	9.44569i	−0.659834	−	0.440887i
$460$		0			0
$461$	6.86998	−	34.5377i	0.319967	−	1.60858i	−0.401314	−	0.915940i	$-0.631447\pi$
$461$	6.86998	−	34.5377i	0.319967	−	1.60858i	0.721281	−	0.692642i	$-0.243553\pi$
$462$		0			0
$463$	20.0285	−	20.0285i	0.930804	−	0.930804i	−0.0669525	−	0.997756i	$-0.521328\pi$
$463$	20.0285	−	20.0285i	0.930804	−	0.930804i	0.997756	+	0.0669525i	$0.0213276\pi$
$464$		0			0
$465$	−3.24293	−	3.24293i	−0.150387	−	0.150387i
$466$		0			0
$467$	15.7542	+	3.13370i	0.729015	+	0.145010i	0.545624	−	0.838030i	$-0.316293\pi$
$467$	15.7542	+	3.13370i	0.729015	+	0.145010i	0.183391	+	0.983040i	$0.441293\pi$
$468$		0			0
$469$	−1.00869	+	1.50962i	−0.0465771	+	0.0697076i
$470$		0			0
$471$	0.328461	+	0.136053i	0.0151347	+	0.00626898i
$472$		0			0
$473$	11.2229	−	4.64868i	0.516030	−	0.213747i
$474$		0			0
$475$	−36.9122	+	7.34229i	−1.69365	+	0.336888i
$476$		0			0
$477$	−3.05572	+	2.04177i	−0.139912	+	0.0934861i
$478$		0			0
$479$			30.8222i			1.40830i	0.710050	+	0.704151i	$0.248672\pi$
$479$			30.8222i			1.40830i	−0.710050	+	0.704151i	$0.751328\pi$
$480$		0			0
$481$		−	19.6483i		−	0.895887i
$482$		0			0
$483$	−0.323663	+	0.216265i	−0.0147272	+	0.00984040i
$484$		0			0
$485$	−7.73131	+	1.53785i	−0.351061	+	0.0698303i
$486$		0			0
$487$	33.8967	−	14.0405i	1.53601	−	0.636235i	0.555288	−	0.831658i	$-0.312608\pi$
$487$	33.8967	−	14.0405i	1.53601	−	0.636235i	0.980719	+	0.195423i	$0.0626081\pi$
$488$		0			0
$489$	−26.5945	−	11.0158i	−1.20264	−	0.498151i
$490$		0			0
$491$	−6.13196	+	9.17712i	−0.276731	+	0.414158i	−0.943636	−	0.330985i	$-0.892619\pi$
$491$	−6.13196	+	9.17712i	−0.276731	+	0.414158i	0.666904	+	0.745143i	$0.267619\pi$
$492$		0			0
$493$	−29.0704	−	5.78246i	−1.30926	−	0.260429i
$494$		0			0
$495$	−3.97597	−	3.97597i	−0.178707	−	0.178707i
$496$		0			0
$497$	1.65515	−	1.65515i	0.0742436	−	0.0742436i
$498$		0			0
$499$	2.51984	−	12.6681i	0.112804	−	0.567102i	−0.882501	−	0.470310i	$-0.844142\pi$
$499$	2.51984	−	12.6681i	0.112804	−	0.567102i	0.995305	−	0.0967914i	$-0.0308580\pi$
$500$		0			0
$501$	−24.5836	−	16.4262i	−1.09831	−	0.733869i
$502$		0			0
$503$	5.73399	−	13.8431i	0.255666	−	0.617232i	−0.742977	−	0.669317i	$-0.766587\pi$
$503$	5.73399	−	13.8431i	0.255666	−	0.617232i	0.998643	+	0.0520853i	$0.0165868\pi$
$504$		0			0
$505$	−0.980863	−	2.36801i	−0.0436478	−	0.105375i
$506$		0			0
$507$	0.145730	+	0.732635i	0.00647211	+	0.0325375i
$508$		0			0
$509$	−13.9117	−	20.8204i	−0.616627	−	0.922848i	0.383372	−	0.923594i	$-0.374763\pi$
$509$	−13.9117	−	20.8204i	−0.616627	−	0.922848i	−1.00000		0.000745744i	$0.999763\pi$
$510$		0			0
$511$	3.56648			0.157772
$512$		0			0
$513$	37.7188			1.66533
$514$		0			0
$515$	11.5612	+	17.3025i	0.509446	+	0.762439i
$516$		0			0
$517$	3.78172	+	19.0120i	0.166320	+	0.836146i
$518$		0			0
$519$	−8.10602	−	19.5697i	−0.355815	−	0.859013i
$520$		0			0
$521$	−7.37291	+	17.7998i	−0.323013	+	0.779822i	0.676063	+	0.736844i	$0.263685\pi$
$521$	−7.37291	+	17.7998i	−0.323013	+	0.779822i	−0.999076	+	0.0429783i	$0.986315\pi$
$522$		0			0
$523$	2.21124	+	1.47750i	0.0966907	+	0.0646067i	0.602976	−	0.797760i	$-0.293982\pi$
$523$	2.21124	+	1.47750i	0.0966907	+	0.0646067i	−0.506285	+	0.862366i	$0.668982\pi$
$524$		0			0
$525$	0.571147	−	2.87135i	0.0249269	−	0.125316i
$526$		0			0
$527$	1.92875	−	1.92875i	0.0840176	−	0.0840176i
$528$		0			0
$529$	−15.8886	−	15.8886i	−0.690811	−	0.690811i
$530$		0			0
$531$	−1.63833	−	0.325885i	−0.0710976	−	0.0141422i
$532$		0			0
$533$	−6.50463	+	9.73487i	−0.281747	+	0.421664i
$534$		0			0
$535$	−18.4233	−	7.63117i	−0.796507	−	0.329924i
$536$		0			0
$537$	33.6571	−	13.9412i	1.45241	−	0.601608i
$538$		0			0
$539$	−28.6573	+	5.70030i	−1.23436	+	0.245529i
$540$		0			0
$541$	17.3178	−	11.5714i	0.744550	−	0.497492i	−0.124498	−	0.992220i	$-0.539732\pi$
$541$	17.3178	−	11.5714i	0.744550	−	0.497492i	0.869048	+	0.494728i	$0.164732\pi$
$542$		0			0
$543$		−	23.7884i		−	1.02086i
$544$		0			0
$545$		−	31.1009i		−	1.33222i
$546$		0			0
$547$	−3.42930	+	2.29138i	−0.146626	+	0.0979725i	−0.626719	−	0.779245i	$-0.715603\pi$
$547$	−3.42930	+	2.29138i	−0.146626	+	0.0979725i	0.480093	+	0.877217i	$0.340603\pi$
$548$		0			0
$549$	1.89588	−	0.377115i	0.0809143	−	0.0160949i
$550$		0			0
$551$	60.7513	−	25.1640i	2.58809	−	1.07202i
$552$		0			0
$553$	0.670038	+	0.277539i	0.0284929	+	0.0118022i
$554$		0			0
$555$	16.0604	−	24.0360i	0.681724	−	1.02027i
$556$		0			0
$557$	29.9106	+	5.94959i	1.26735	+	0.252092i	0.782582	−	0.622548i	$-0.213902\pi$
$557$	29.9106	+	5.94959i	1.26735	+	0.252092i	0.484772	+	0.874640i	$0.338902\pi$
$558$		0			0
$559$	−7.17112	−	7.17112i	−0.303306	−	0.303306i
$560$		0			0
$561$	−14.9533	+	14.9533i	−0.631328	+	0.631328i
$562$		0			0
$563$	−2.46552	+	12.3950i	−0.103909	+	0.522387i	0.893412	+	0.449239i	$0.148305\pi$
$563$	−2.46552	+	12.3950i	−0.103909	+	0.522387i	−0.997321	+	0.0731484i	$0.976695\pi$
$564$		0			0
$565$	−17.2674	−	11.5377i	−0.726445	−	0.485395i
$566$		0			0
$567$	−0.966598	+	2.33357i	−0.0405933	+	0.0980008i
$568$		0			0
$569$	1.98587	+	4.79431i	0.0832520	+	0.200988i	0.960024	−	0.279919i	$-0.0903075\pi$
$569$	1.98587	+	4.79431i	0.0832520	+	0.200988i	−0.876772	+	0.480907i	$0.840308\pi$
$570$		0			0
$571$	−5.46069	−	27.4528i	−0.228523	−	1.14886i	−0.909226	−	0.416303i	$-0.863326\pi$
$571$	−5.46069	−	27.4528i	−0.228523	−	1.14886i	0.680703	−	0.732559i	$-0.261674\pi$
$572$		0			0
$573$	−5.98693	−	8.96008i	−0.250108	−	0.374313i
$574$		0			0
$575$	−3.98647			−0.166247
$576$		0			0
$577$	−5.80892			−0.241829			−0.120914	−	0.992663i	$-0.538583\pi$
$577$	−5.80892			−0.241829			−0.120914	+	0.992663i	$0.538583\pi$
$578$		0			0
$579$	2.80363	+	4.19593i	0.116515	+	0.174377i
$580$		0			0
$581$	−0.960477	−	4.82865i	−0.0398473	−	0.200326i
$582$		0			0
$583$	14.5602	+	35.1515i	0.603023	+	1.45583i
$584$		0			0
$585$	−1.79643	+	4.33696i	−0.0742731	+	0.179311i
$586$		0			0
$587$	−38.7045	−	25.8615i	−1.59751	−	1.06742i	−0.953065	−	0.302766i	$-0.902090\pi$
$587$	−38.7045	−	25.8615i	−1.59751	−	1.06742i	−0.644441	−	0.764654i	$-0.722910\pi$
$588$		0			0
$589$	−1.18056	+	5.93509i	−0.0486443	+	0.244551i
$590$		0			0
$591$	−17.8238	+	17.8238i	−0.733175	+	0.733175i
$592$		0			0
$593$	10.6123	+	10.6123i	0.435796	+	0.435796i	0.890594	−	0.454799i	$-0.150289\pi$
$593$	10.6123	+	10.6123i	0.435796	+	0.435796i	−0.454799	+	0.890594i	$0.650289\pi$
$594$		0			0
$595$	3.26719	+	0.649884i	0.133942	+	0.0266426i
$596$		0			0
$597$	−3.82683	+	5.72726i	−0.156622	+	0.234401i
$598$		0			0
$599$	−37.1396	−	15.3837i	−1.51748	−	0.628561i	−0.540396	−	0.841411i	$-0.681726\pi$
$599$	−37.1396	−	15.3837i	−1.51748	−	0.628561i	−0.977085	+	0.212850i	$0.931726\pi$
$600$		0			0
$601$	−10.9322	+	4.52827i	−0.445934	+	0.184712i	−0.594339	−	0.804215i	$-0.702586\pi$
$601$	−10.9322	+	4.52827i	−0.445934	+	0.184712i	0.148405	+	0.988927i	$0.452586\pi$
$602$		0			0
$603$	2.19580	−	0.436772i	0.0894199	−	0.0177867i
$604$		0			0
$605$	−18.7998	+	12.5616i	−0.764322	+	0.510704i
$606$		0			0
$607$			20.3426i			0.825679i	0.910804	+	0.412840i	$0.135463\pi$
$607$			20.3426i			0.825679i	−0.910804	+	0.412840i	$0.864537\pi$
$608$		0			0
$609$			5.11513i			0.207275i
$610$		0			0
$611$	13.4559	−	8.99093i	0.544366	−	0.363734i
$612$		0			0
$613$	26.9544	−	5.36156i	1.08868	−	0.216552i	0.382053	−	0.924140i	$-0.375217\pi$
$613$	26.9544	−	5.36156i	1.08868	−	0.216552i	0.706625	+	0.707589i	$0.250217\pi$
$614$		0			0
$615$	−15.9144	+	6.59195i	−0.641730	+	0.265813i
$616$		0			0
$617$	12.8642	+	5.32854i	0.517895	+	0.214519i	0.626292	−	0.779589i	$-0.284572\pi$
$617$	12.8642	+	5.32854i	0.517895	+	0.214519i	−0.108397	+	0.994108i	$0.534572\pi$
$618$		0			0
$619$	19.3117	−	28.9020i	0.776204	−	1.16167i	−0.206854	−	0.978372i	$-0.566322\pi$
$619$	19.3117	−	28.9020i	0.776204	−	1.16167i	0.983057	−	0.183299i	$-0.0586776\pi$
$620$		0			0
$621$	3.91854	+	0.779446i	0.157246	+	0.0312781i
$622$		0			0
$623$	−0.417200	−	0.417200i	−0.0167148	−	0.0167148i
$624$		0			0
$625$	−15.8365	+	15.8365i	−0.633460	+	0.633460i
$626$		0			0
$627$	9.15273	−	46.0139i	0.365525	−	1.83762i
$628$		0			0
$629$	14.2956	+	9.55198i	0.570001	+	0.380862i
$630$		0			0
$631$	10.3488	−	24.9842i	0.411980	−	0.994607i	−0.572626	−	0.819817i	$-0.694075\pi$
$631$	10.3488	−	24.9842i	0.411980	−	0.994607i	0.984606	−	0.174790i	$-0.0559246\pi$
$632$		0			0
$633$	−12.7329	−	30.7398i	−0.506085	−	1.22180i
$634$		0			0
$635$	8.30076	+	41.7307i	0.329406	+	1.65603i
$636$		0			0
$637$	13.5523	+	20.2824i	0.536961	+	0.803620i
$638$		0			0
$639$	−2.88636			−0.114183
$640$		0			0
$641$	−26.5599			−1.04905			−0.524527	−	0.851394i	$-0.675758\pi$
$641$	−26.5599			−1.04905			−0.524527	+	0.851394i	$0.675758\pi$
$642$		0			0
$643$	7.23987	+	10.8352i	0.285513	+	0.427300i	0.946308	−	0.323266i	$-0.104781\pi$
$643$	7.23987	+	10.8352i	0.285513	+	0.427300i	−0.660795	+	0.750566i	$0.729781\pi$
$644$		0			0
$645$	−2.91091	−	14.6341i	−0.114617	−	0.576218i
$646$		0			0
$647$	−4.72206	−	11.4001i	−0.185643	−	0.448183i	0.803469	−	0.595347i	$-0.202985\pi$
$647$	−4.72206	−	11.4001i	−0.185643	−	0.448183i	−0.989112	+	0.147164i	$0.952985\pi$
$648$		0			0
$649$	−6.61803	+	15.9773i	−0.259780	+	0.627165i
$650$		0			0
$651$	−0.391396	−	0.261522i	−0.0153400	−	0.0102499i
$652$		0			0
$653$	1.67322	−	8.41182i	0.0654780	−	0.329180i	−0.934137	−	0.356914i	$-0.883829\pi$
$653$	1.67322	−	8.41182i	0.0654780	−	0.329180i	0.999615	+	0.0277336i	$0.00882902\pi$
$654$		0			0
$655$	−32.9993	+	32.9993i	−1.28939	+	1.28939i
$656$		0			0
$657$	−3.10974	−	3.10974i	−0.121322	−	0.121322i
$658$		0			0
$659$	30.9667	+	6.15965i	1.20629	+	0.239946i	0.756985	−	0.653432i	$-0.226672\pi$
$659$	30.9667	+	6.15965i	1.20629	+	0.239946i	0.449305	+	0.893378i	$0.351672\pi$
$660$		0			0
$661$	12.7193	−	19.0357i	0.494722	−	0.740403i	−0.497147	−	0.867666i	$-0.665619\pi$
$661$	12.7193	−	19.0357i	0.494722	−	0.740403i	0.991869	+	0.127263i	$0.0406192\pi$
$662$		0			0
$663$	16.3109	+	6.75621i	0.633464	+	0.262389i
$664$		0			0
$665$	−6.82777	+	2.82815i	−0.264769	+	0.109671i
$666$		0			0
$667$	6.83135	−	1.35884i	0.264511	−	0.0526145i
$668$		0			0
$669$	24.2836	−	16.2258i	0.938857	−	0.627324i
$670$		0			0
$671$		−	20.0124i		−	0.772569i
$672$		0			0
$673$			24.9965i			0.963543i	0.876297	+	0.481772i	$0.160007\pi$
$673$			24.9965i			0.963543i	−0.876297	+	0.481772i	$0.839993\pi$
$674$		0			0
$675$	−24.9840	+	16.6938i	−0.961634	+	0.642543i
$676$		0			0
$677$	33.5580	−	6.67509i	1.28974	−	0.256545i	0.497877	−	0.867247i	$-0.334113\pi$
$677$	33.5580	−	6.67509i	1.28974	−	0.256545i	0.791860	+	0.610703i	$0.209113\pi$
$678$		0			0
$679$	−0.747501	+	0.309625i	−0.0286865	+	0.0118823i
$680$		0			0
$681$	24.1200	+	9.99084i	0.924281	+	0.382850i
$682$		0			0
$683$	−0.339438	+	0.508005i	−0.0129882	+	0.0194383i	−0.837907	−	0.545813i	$-0.816221\pi$
$683$	−0.339438	+	0.508005i	−0.0129882	+	0.0194383i	0.824919	+	0.565251i	$0.191221\pi$
$684$		0			0
$685$	−16.7489	−	3.33156i	−0.639942	−	0.127292i
$686$		0			0
$687$	1.34203	+	1.34203i	0.0512016	+	0.0512016i
$688$		0			0
$689$	22.4608	−	22.4608i	0.855688	−	0.855688i
$690$		0			0
$691$	−8.80950	+	44.2884i	−0.335129	+	1.68481i	0.334725	+	0.942316i	$0.391357\pi$
$691$	−8.80950	+	44.2884i	−0.335129	+	1.68481i	−0.669854	+	0.742492i	$0.733643\pi$
$692$		0			0
$693$	−0.479869	−	0.320638i	−0.0182287	−	0.0121800i
$694$		0			0
$695$	−6.04935	+	14.6044i	−0.229465	+	0.553977i
$696$		0			0
$697$	−3.92060	−	9.46516i	−0.148503	−	0.358518i
$698$		0			0
$699$	−1.10749	−	5.56774i	−0.0418892	−	0.210591i
$700$		0			0
$701$	18.1076	+	27.1000i	0.683915	+	1.02355i	0.997265	+	0.0739139i	$0.0235490\pi$
$701$	18.1076	+	27.1000i	0.683915	+	1.02355i	−0.313349	+	0.949638i	$0.601451\pi$
$702$		0			0
$703$	−38.1433			−1.43860
$704$		0			0
$705$	23.8098			0.896730
$706$		0			0
$707$	−0.146159	−	0.218742i	−0.00549687	−	0.00822665i
$708$		0			0
$709$	8.67202	+	43.5972i	0.325684	+	1.63733i	0.702963	+	0.711226i	$0.251860\pi$
$709$	8.67202	+	43.5972i	0.325684	+	1.63733i	−0.377279	+	0.926100i	$0.623140\pi$
$710$		0			0
$711$	−0.342234	−	0.826225i	−0.0128348	−	0.0309859i
$712$		0			0
$713$	−0.245293	+	0.592190i	−0.00918630	+	0.0221777i
$714$		0			0
$715$	40.4089	+	27.0004i	1.51121	+	1.00976i
$716$		0			0
$717$	−2.46262	+	12.3804i	−0.0919681	+	0.462355i
$718$		0			0
$719$	10.7756	−	10.7756i	0.401864	−	0.401864i	−0.477026	−	0.878889i	$-0.658285\pi$
$719$	10.7756	−	10.7756i	0.401864	−	0.401864i	0.878889	+	0.477026i	$0.158285\pi$
$720$		0			0
$721$	1.51031	+	1.51031i	0.0562467	+	0.0562467i
$722$		0			0
$723$	−13.3646	−	2.65838i	−0.497033	−	0.0988661i
$724$		0			0
$725$	−29.1029	+	43.5556i	−1.08085	+	1.61761i
$726$		0			0
$727$	−8.49854	−	3.52021i	−0.315193	−	0.130557i	0.219478	−	0.975617i	$-0.429565\pi$
$727$	−8.49854	−	3.52021i	−0.315193	−	0.130557i	−0.534671	+	0.845060i	$0.679565\pi$
$728$		0			0
$729$	27.3572	−	11.3317i	1.01323	−	0.419693i
$730$		0			0
$731$	8.70372	−	1.73128i	0.321919	−	0.0640336i
$732$		0			0
$733$	−5.58778	+	3.73364i	−0.206389	+	0.137905i	−0.654469	−	0.756088i	$-0.727108\pi$
$733$	−5.58778	+	3.73364i	−0.206389	+	0.137905i	0.448080	+	0.893993i	$0.352108\pi$
$734$		0			0
$735$			35.8893i			1.32380i
$736$		0			0
$737$		−	23.1782i		−	0.853780i
$738$		0			0
$739$	28.0412	−	18.7365i	1.03151	−	0.689235i	0.0799848	−	0.996796i	$-0.474513\pi$
$739$	28.0412	−	18.7365i	1.03151	−	0.689235i	0.951528	+	0.307561i	$0.0995128\pi$
$740$		0			0
$741$	−38.4150	+	7.64121i	−1.41121	+	0.280707i
$742$		0			0
$743$	−31.3039	+	12.9665i	−1.14843	+	0.475694i	−0.874006	−	0.485915i	$-0.838486\pi$
$743$	−31.3039	+	12.9665i	−1.14843	+	0.475694i	−0.274421	+	0.961610i	$0.588486\pi$
$744$		0			0
$745$	−28.6537	−	11.8687i	−1.04979	−	0.434837i
$746$		0			0
$747$	−3.37279	+	5.04774i	−0.123404	+	0.184687i
$748$		0			0
$749$	−2.00744	−	0.399305i	−0.0733503	−	0.0145903i
$750$		0			0
$751$	22.7813	+	22.7813i	0.831303	+	0.831303i	0.987695	−	0.156392i	$-0.0499864\pi$
$751$	22.7813	+	22.7813i	0.831303	+	0.831303i	−0.156392	+	0.987695i	$0.549986\pi$
$752$		0			0
$753$	2.55130	−	2.55130i	0.0929747	−	0.0929747i
$754$		0			0
$755$	10.4184	−	52.3769i	0.379165	−	1.90619i
$756$		0			0
$757$	−35.0984	−	23.4520i	−1.27567	−	0.852378i	−0.281437	−	0.959580i	$-0.590811\pi$
$757$	−35.0984	−	23.4520i	−1.27567	−	0.852378i	−0.994237	+	0.107202i	$0.965811\pi$
$758$		0			0
$759$	1.90172	−	4.59116i	0.0690281	−	0.166649i
$760$		0			0
$761$	−0.451808	−	1.09076i	−0.0163780	−	0.0395401i	0.915479	−	0.402366i	$-0.131812\pi$
$761$	−0.451808	−	1.09076i	−0.0163780	−	0.0395401i	−0.931857	+	0.362826i	$0.881812\pi$
$762$		0			0
$763$	−0.622768	−	3.13087i	−0.0225457	−	0.113345i
$764$		0			0
$765$	−2.28212	−	3.41543i	−0.0825101	−	0.123485i
$766$		0			0
$767$	14.4378			0.521318
$768$		0			0
$769$	−46.3441			−1.67121			−0.835605	−	0.549331i	$-0.814883\pi$
$769$	−46.3441			−1.67121			−0.835605	+	0.549331i	$0.814883\pi$
$770$		0			0
$771$	17.0391	+	25.5008i	0.613647	+	0.918388i
$772$		0			0
$773$	−3.29586	−	16.5694i	−0.118544	−	0.595960i	−0.993696	−	0.112111i	$-0.964239\pi$
$773$	−3.29586	−	16.5694i	−0.118544	−	0.595960i	0.875152	−	0.483848i	$-0.160761\pi$
$774$		0			0
$775$	−1.84481	−	4.45375i	−0.0662674	−	0.159984i
$776$		0			0
$777$	1.13546	−	2.74125i	0.0407346	−	0.0983420i
$778$		0			0
$779$	18.8983	+	12.6274i	0.677101	+	0.452425i
$780$		0			0
$781$	−5.82972	+	29.3080i	−0.208604	+	1.04872i
$782$		0			0
$783$	37.1231	−	37.1231i	1.32667	−	1.32667i
$784$		0			0
$785$	0.505546	+	0.505546i	0.0180437	+	0.0180437i
$786$		0			0
$787$	−29.7168	−	5.91104i	−1.05929	−	0.210706i	−0.365447	−	0.930832i	$-0.619084\pi$
$787$	−29.7168	−	5.91104i	−1.05929	−	0.210706i	−0.693843	+	0.720126i	$0.744084\pi$
$788$		0			0
$789$	5.65450	−	8.46256i	0.201306	−	0.301275i
$790$		0			0
$791$	−1.96931	−	0.815714i	−0.0700205	−	0.0290034i
$792$		0			0
$793$	−15.4357	+	6.39367i	−0.548137	+	0.227046i
$794$		0			0
$795$	45.8358	−	9.11731i	1.62563	−	0.323358i
$796$		0			0
$797$	−25.2213	+	16.8523i	−0.893385	+	0.596940i	−0.915279	−	0.402820i	$-0.868030\pi$
$797$	−25.2213	+	16.8523i	−0.893385	+	0.596940i	0.0218948	+	0.999760i	$0.493030\pi$
$798$		0			0
$799$			14.1610i			0.500981i
$800$		0			0
$801$			0.727542i			0.0257064i
$802$		0			0
$803$	−37.8570	+	25.2952i	−1.33594	+	0.892649i
$804$		0			0
$805$	−0.767767	+	0.152718i	−0.0270602	+	0.00538261i
$806$		0			0
$807$	−15.3365	+	6.35261i	−0.539872	+	0.223622i
$808$		0			0
$809$	−2.77252	−	1.14841i	−0.0974765	−	0.0403761i	0.333412	−	0.942781i	$-0.391800\pi$
$809$	−2.77252	−	1.14841i	−0.0974765	−	0.0403761i	−0.430889	+	0.902405i	$0.641800\pi$
$810$		0			0
$811$	−23.3343	+	34.9223i	−0.819378	+	1.22629i	0.151913	+	0.988394i	$0.451457\pi$
$811$	−23.3343	+	34.9223i	−0.819378	+	1.22629i	−0.971291	+	0.237893i	$0.923543\pi$
$812$		0			0
$813$	−9.33230	−	1.85631i	−0.327298	−	0.0651036i
$814$		0			0
$815$	−40.9326	−	40.9326i	−1.43381	−	1.43381i
$816$		0			0
$817$	−13.9213	+	13.9213i	−0.487044	+	0.487044i
$818$		0			0
$819$	−0.0939990	+	0.472565i	−0.00328459	+	0.0165128i
$820$		0			0
$821$	32.4829	+	21.7044i	1.13366	+	0.757487i	0.973292	−	0.229570i	$-0.0737320\pi$
$821$	32.4829	+	21.7044i	1.13366	+	0.757487i	0.160368	+	0.987057i	$0.448732\pi$
$822$		0			0
$823$	−13.3449	+	32.2174i	−0.465173	+	1.12303i	0.501073	+	0.865405i	$0.332939\pi$
$823$	−13.3449	+	32.2174i	−0.465173	+	1.12303i	−0.966246	+	0.257622i	$0.917061\pi$
$824$		0			0
$825$	14.3025	+	34.5293i	0.497949	+	1.20215i
$826$		0			0
$827$	7.94105	+	39.9224i	0.276137	+	1.38824i	0.830990	+	0.556288i	$0.187775\pi$
$827$	7.94105	+	39.9224i	0.276137	+	1.38824i	−0.554852	+	0.831949i	$0.687225\pi$
$828$		0			0
$829$	31.8213	+	47.6240i	1.10520	+	1.65405i	0.638460	+	0.769655i	$0.279572\pi$
$829$	31.8213	+	47.6240i	1.10520	+	1.65405i	0.466740	+	0.884395i	$0.345428\pi$
$830$		0			0
$831$	−3.05702			−0.106047
$832$		0			0
$833$	−21.3453			−0.739571
$834$		0			0
$835$	−33.0328	−	49.4371i	−1.14315	−	1.71084i
$836$		0			0
$837$	0.942559	+	4.73857i	0.0325796	+	0.163789i
$838$		0			0
$839$	14.5831	+	35.2068i	0.503465	+	1.21547i	0.947585	+	0.319505i	$0.103517\pi$
$839$	14.5831	+	35.2068i	0.503465	+	1.21547i	−0.444119	+	0.895968i	$0.646483\pi$
$840$		0			0
$841$	23.9274	−	57.7659i	0.825083	−	1.99193i
$842$		0			0
$843$	29.8816	+	19.9663i	1.02918	+	0.687675i
$844$		0			0
$845$	−0.293061	+	1.47332i	−0.0100816	+	0.0506836i
$846$		0			0
$847$	−1.64101	+	1.64101i	−0.0563856	+	0.0563856i
$848$		0			0
$849$	−0.178230	−	0.178230i	−0.00611684	−	0.00611684i
$850$		0			0
$851$	−3.96263	−	0.788217i	−0.135837	−	0.0270197i
$852$		0			0
$853$	30.9971	−	46.3904i	1.06132	−	1.58838i	0.284474	−	0.958684i	$-0.408181\pi$
$853$	30.9971	−	46.3904i	1.06132	−	1.58838i	0.776845	−	0.629692i	$-0.216819\pi$
$854$		0			0
$855$	8.41933	+	3.48740i	0.287935	+	0.119267i
$856$		0			0
$857$	15.6625	−	6.48761i	0.535020	−	0.221612i	−0.0987804	−	0.995109i	$-0.531494\pi$
$857$	15.6625	−	6.48761i	0.535020	−	0.221612i	0.633800	+	0.773497i	$0.281494\pi$
$858$		0			0
$859$	5.32236	−	1.05868i	0.181597	−	0.0361218i	−0.103454	−	0.994634i	$-0.532990\pi$
$859$	5.32236	−	1.05868i	0.181597	−	0.0361218i	0.285051	+	0.958512i	$0.407990\pi$
$860$		0			0
$861$	−1.47007	+	0.982270i	−0.0500999	+	0.0334757i
$862$		0			0
$863$			12.0786i			0.411160i	0.978640	+	0.205580i	$0.0659081\pi$
$863$			12.0786i			0.411160i	−0.978640	+	0.205580i	$0.934092\pi$
$864$		0			0
$865$		−	42.5967i		−	1.44833i
$866$		0			0
$867$	9.90454	−	6.61800i	0.336376	−	0.224759i
$868$		0			0
$869$	−9.08067	+	1.80626i	−0.308041	+	0.0612731i
$870$		0			0
$871$	−17.8775	+	7.40510i	−0.605756	+	0.250912i
$872$		0			0
$873$	0.921745	+	0.381799i	0.0311963	+	0.0129219i
$874$		0			0
$875$	0.284063	−	0.425131i	0.00960310	−	0.0143721i
$876$		0			0
$877$	19.9561	+	3.96951i	0.673868	+	0.134041i	0.520151	−	0.854074i	$-0.325876\pi$
$877$	19.9561	+	3.96951i	0.673868	+	0.134041i	0.153717	+	0.988115i	$0.450876\pi$
$878$		0			0
$879$	−9.49451	−	9.49451i	−0.320242	−	0.320242i
$880$		0			0
$881$	20.2066	−	20.2066i	0.680777	−	0.680777i	−0.279398	−	0.960175i	$-0.590135\pi$
$881$	20.2066	−	20.2066i	0.680777	−	0.680777i	0.960175	+	0.279398i	$0.0901350\pi$
$882$		0			0
$883$	2.71690	−	13.6588i	0.0914310	−	0.459655i	−0.907762	−	0.419486i	$-0.862210\pi$
$883$	2.71690	−	13.6588i	0.0914310	−	0.459655i	0.999193	−	0.0401690i	$-0.0127896\pi$
$884$		0			0
$885$	17.6619	+	11.8013i	0.593699	+	0.396697i
$886$		0			0
$887$	2.29326	−	5.53641i	0.0770000	−	0.185894i	−0.880692	−	0.473689i	$-0.842922\pi$
$887$	2.29326	−	5.53641i	0.0770000	−	0.185894i	0.957692	+	0.287795i	$0.0929221\pi$
$888$		0			0
$889$	1.67124	+	4.03474i	0.0560517	+	0.135321i
$890$		0			0
$891$	−6.29074	−	31.6257i	−0.210748	−	1.05950i
$892$		0			0
$893$	−17.4541	−	26.1219i	−0.584078	−	0.874134i
$894$		0			0
$895$	73.2605			2.44883
$896$		0			0
$897$	−4.14877			−0.138523
$898$		0			0
$899$	4.67944	+	7.00328i	0.156068	+	0.233572i
$900$		0			0
$901$	5.42256	+	27.2611i	0.180652	+	0.908198i
$902$		0			0
$903$	−0.586071	−	1.41490i	−0.0195032	−	0.0470849i
$904$		0			0
$905$	18.3068	−	44.1966i	0.608539	−	1.46914i
$906$		0			0
$907$	−41.9267	−	28.0145i	−1.39215	−	0.930207i	−0.999947	−	0.0103304i	$-0.996712\pi$
$907$	−41.9267	−	28.0145i	−1.39215	−	0.930207i	−0.392207	−	0.919877i	$-0.628288\pi$
$908$		0			0
$909$	−0.0632879	+	0.318170i	−0.00209913	+	0.0105530i
$910$		0			0
$911$	−10.6573	+	10.6573i	−0.353092	+	0.353092i	−0.861259	−	0.508167i	$-0.830323\pi$
$911$	−10.6573	+	10.6573i	−0.353092	+	0.353092i	0.508167	+	0.861259i	$0.330323\pi$
$912$		0			0
$913$	44.4423	+	44.4423i	1.47082	+	1.47082i
$914$		0			0
$915$	−24.1088	−	4.79553i	−0.797011	−	0.158535i
$916$		0			0
$917$	−2.66119	+	3.98276i	−0.0878804	+	0.131522i
$918$		0			0
$919$	48.0863	+	19.9180i	1.58622	+	0.657034i	0.989383	−	0.145328i	$-0.0464238\pi$
$919$	48.0863	+	19.9180i	1.58622	+	0.657034i	0.596837	+	0.802362i	$0.296424\pi$
$920$		0			0
$921$	−50.9061	+	21.0860i	−1.67741	+	0.694807i
$922$		0			0
$923$	24.4680	−	4.86698i	0.805373	−	0.160199i
$924$		0			0
$925$	25.2651	−	16.8816i	0.830712	−	0.555064i
$926$		0			0
$927$		−	2.63378i		−	0.0865046i
$928$		0			0
$929$			47.7676i			1.56721i	0.621262	+	0.783603i	$0.286620\pi$
$929$			47.7676i			1.56721i	−0.621262	+	0.783603i	$0.713380\pi$
$930$		0			0
$931$	39.3743	−	26.3090i	1.29044	−	0.862244i
$932$		0			0
$933$	20.7883	−	4.13505i	0.680579	−	0.135375i
$934$		0			0
$935$	−39.2894	+	16.2742i	−1.28490	+	0.532223i
$936$		0			0
$937$	−40.2328	−	16.6650i	−1.31435	−	0.544421i	−0.388198	−	0.921576i	$-0.626902\pi$
$937$	−40.2328	−	16.6650i	−1.31435	−	0.544421i	−0.926150	+	0.377155i	$0.876902\pi$
$938$		0			0
$939$	0.376223	−	0.563057i	0.0122776	−	0.0183747i
$940$		0			0
$941$	−38.6865	−	7.69522i	−1.26114	−	0.250857i	−0.481147	−	0.876640i	$-0.659780\pi$
$941$	−38.6865	−	7.69522i	−1.26114	−	0.250857i	−0.779997	+	0.625783i	$0.784780\pi$
$942$		0			0
$943$	1.70237	+	1.70237i	0.0554367	+	0.0554367i
$944$		0			0
$945$	−4.17222	+	4.17222i	−0.135722	+	0.135722i
$946$		0			0
$947$	−3.32492	+	16.7155i	−0.108045	+	0.543180i	0.888410	+	0.459052i	$0.151811\pi$
$947$	−3.32492	+	16.7155i	−0.108045	+	0.543180i	−0.996455	+	0.0841288i	$0.973189\pi$
$948$		0			0
$949$	31.6051	+	21.1179i	1.02595	+	0.685515i
$950$		0			0
$951$	10.3445	−	24.9738i	0.335443	−	0.809830i
$952$		0			0
$953$	−0.606561	−	1.46437i	−0.0196484	−	0.0474355i	0.913751	−	0.406275i	$-0.133173\pi$
$953$	−0.606561	−	1.46437i	−0.0196484	−	0.0474355i	−0.933399	+	0.358840i	$0.883173\pi$
$954$		0			0
$955$	−4.22775	−	21.2543i	−0.136807	−	0.687774i
$956$		0			0
$957$	−36.2790	−	54.2953i	−1.17273	−	1.75512i
$958$		0			0
$959$	−1.75279			−0.0566005
$960$		0			0
$961$	30.2249			0.974996
$962$		0			0
$963$	1.40219	+	2.09853i	0.0451849	+	0.0676240i
$964$		0			0
$965$	1.97982	+	9.95324i	0.0637327	+	0.320406i
$966$		0			0
$967$	−20.5832	−	49.6922i	−0.661910	−	1.59799i	−0.794806	−	0.606863i	$-0.792428\pi$
$967$	−20.5832	−	49.6922i	−0.661910	−	1.59799i	0.132896	−	0.991130i	$-0.457572\pi$
$968$		0			0
$969$	13.1158	−	31.6644i	0.421341	−	1.01721i
$970$		0			0
$971$	−44.7859	−	29.9250i	−1.43725	−	0.960338i	−0.998080	−	0.0619328i	$-0.980274\pi$
$971$	−44.7859	−	29.9250i	−1.43725	−	0.960338i	−0.439167	−	0.898405i	$-0.644726\pi$
$972$		0			0
$973$	−0.316535	+	1.59133i	−0.0101477	+	0.0510157i
$974$		0			0
$975$	22.0632	−	22.0632i	0.706588	−	0.706588i
$976$		0			0
$977$	10.3049	+	10.3049i	0.329682	+	0.329682i	0.852466	−	0.522783i	$-0.175106\pi$
$977$	10.3049	+	10.3049i	0.329682	+	0.329682i	−0.522783	+	0.852466i	$0.675106\pi$
$978$		0			0
$979$	7.38742	+	1.46945i	0.236103	+	0.0469638i
$980$		0			0
$981$	−2.18690	+	3.27292i	−0.0698223	+	0.104496i
$982$		0			0
$983$	3.68355	+	1.52578i	0.117487	+	0.0486647i	0.440653	−	0.897678i	$-0.354747\pi$
$983$	3.68355	+	1.52578i	0.117487	+	0.0486647i	−0.323166	+	0.946342i	$0.604747\pi$
$984$		0			0
$985$	−46.8317	+	19.3983i	−1.49218	+	0.618082i
$986$		0			0
$987$	2.39689	−	0.476771i	0.0762938	−	0.0151758i
$988$		0			0
$989$	−1.73393	+	1.15858i	−0.0551359	+	0.0368406i
$990$		0			0
$991$		−	22.4878i		−	0.714348i	−0.934038	−	0.357174i	$-0.883740\pi$
$991$		−	22.4878i		−	0.714348i	0.934038	−	0.357174i	$-0.116260\pi$
$992$		0			0
$993$			52.9500i			1.68032i
$994$		0			0
$995$	−11.5174	+	7.69569i	−0.365127	+	0.243970i
$996$		0			0
$997$	36.8027	−	7.32050i	1.16555	−	0.231843i	0.425860	−	0.904789i	$-0.359972\pi$
$997$	36.8027	−	7.32050i	1.16555	−	0.231843i	0.739691	+	0.672946i	$0.234972\pi$
$998$		0			0
$999$	−28.1354	+	11.6540i	−0.890163	+	0.368718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.17.6		56
4.3	odd	2		64.2.i.a.45.6	yes	56
8.3	odd	2		512.2.i.b.289.6		56
8.5	even	2		512.2.i.a.289.2		56
12.11	even	2		576.2.bd.a.109.2		56
64.5	even	16		512.2.i.a.225.2		56
64.27	odd	16		64.2.i.a.37.6	✓	56
64.37	even	16	inner	256.2.i.a.241.6		56
64.59	odd	16		512.2.i.b.225.6		56
192.155	even	16		576.2.bd.a.37.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.6	✓	56	64.27	odd	16
64.2.i.a.45.6	yes	56	4.3	odd	2
256.2.i.a.17.6		56	1.1	even	1	trivial
256.2.i.a.241.6		56	64.37	even	16	inner
512.2.i.a.225.2		56	64.5	even	16
512.2.i.a.289.2		56	8.5	even	2
512.2.i.b.225.6		56	64.59	odd	16
512.2.i.b.289.6		56	8.3	odd	2
576.2.bd.a.37.2		56	192.155	even	16
576.2.bd.a.109.2		56	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.894167 + 1.33822i) q^{3} +(0.631428 + 3.17440i) q^{5} +(0.127129 + 0.306917i) q^{7} +(0.156763 - 0.378460i) q^{9} +O(q^{10})\)	\(q+(0.894167 + 1.33822i) q^{3} +(0.631428 + 3.17440i) q^{5} +(0.127129 + 0.306917i) q^{7} +(0.156763 - 0.378460i) q^{9} +(-3.52624 - 2.35616i) q^{11} +(-0.690738 + 3.47257i) q^{13} +(-3.68343 + 3.68343i) q^{15} +(-2.19074 - 2.19074i) q^{17} +(6.74130 + 1.34093i) q^{19} +(-0.297047 + 0.444562i) q^{21} +(0.672631 + 0.278613i) q^{23} +(-5.05873 + 2.09540i) q^{25} +(5.38223 - 1.07059i) q^{27} +(7.95458 - 5.31508i) q^{29} +0.880409i q^{31} -6.82567i q^{33} +(-0.894006 + 0.597355i) q^{35} +(-5.44280 + 1.08264i) q^{37} +(-5.26469 + 2.18070i) q^{39} +(3.05507 + 1.26545i) q^{41} +(-1.59134 + 2.38161i) q^{43} +(1.30037 + 0.258659i) q^{45} +(-3.23201 - 3.23201i) q^{47} +(4.87171 - 4.87171i) q^{49} +(0.972796 - 4.89058i) q^{51} +(-7.45949 - 4.98427i) q^{53} +(5.25283 - 12.6815i) q^{55} +(4.23340 + 10.2203i) q^{57} +(-0.795535 - 3.99942i) q^{59} +(2.62163 + 3.92355i) q^{61} +0.136085 q^{63} -11.4595 q^{65} +(3.03636 + 4.54423i) q^{67} +(0.228601 + 1.14925i) q^{69} +(-2.69641 - 6.50971i) q^{71} +(4.10841 - 9.91857i) q^{73} +(-7.32745 - 4.89605i) q^{75} +(0.274857 - 1.38180i) q^{77} +(1.54370 - 1.54370i) q^{79} +(5.37632 + 5.37632i) q^{81} +(-14.5352 - 2.89122i) q^{83} +(5.57100 - 8.33759i) q^{85} +(14.2254 + 5.89237i) q^{87} +(-1.64085 + 0.679662i) q^{89} +(-1.15360 + 0.229466i) q^{91} +(-1.17818 + 0.787233i) q^{93} +22.2463i q^{95} +2.43552i q^{97} +(-1.44450 + 0.965182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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